This is a very detailed topic and I am on mobile so I am sure I will leave some things out, but I’ll try to sketch a decent picture. The truth, so far as we could possibly identify it a thousand years later, is that neither one of these narratives is true.
In regards to the first, “proto-colonialism,” the reality is that the Crusades were first and foremost a religious pilgrimage. While there were some, especially among the nobility (aka “the barons”) who clearly were seeking personal gain, such as Bohemond of Taranto or Baldwin of Bolougne, a great many participants had no intention of remaining in the Levant upon completion of the crusade. Many simply visited the holy sites and made their way home. Overall, motivations were as individual as each person, but the overall picture is one in which most completed what they believed was their religious duty and, it having been fulfilled, packed up and left. This, of course, left the new crusader states chronically short of manpower. More importantly, it meant that rather than even accidentally becoming a colonial project wherein Francia or Germany was transplanted to Outremer, the native culture absorbed the newcomers and a sort of ‘Franco-Syrian’ identify was slowly established over the next century. Further information on all of the above can be found in Zoe Oldenburg’s The Crusades
Additionally, the Crusades at first merited nothing more than a local response. The leaders of the cities which were targeted of course were alarmed and then were dispossessed or killed, but the first crusade failed to generate any sizable moral or political response in neighboring regions. The response in Mosul was muted, and it was barely noteworthy in Baghdad. The Seljuqs of course fought because it was their land and armies being attacked, but even they were fractured politically and were fighting each other even as the crusaders arrived. The seizure of Jerusalem generated a reaction from Cairo only because the Fatimids had controlled the territory directly, following a lengthy war with the Seljuqs to keep it. After the crusader victory at Ascalon however, they could not even seize the city itself and Fatimids were content to hold on to it for another 50 years. Even Damascus was content to make accommodations with the new arrivals, becoming semi-allied with Jerusalem until the immensely ill-advised decision during the Second Crusade to attack Damascus rather than Edessa as planned. Ultimately it was not until almost a half century after the first crusade that Muslims in Syria and Iraq became galvanized in a significant way toward fighting off the crusader, and a lot of that was due to the personal dynamism of Imad and Nur ad-Din Zengi and contemporary preachers who shamed the people of Mosul and Baghdad into doing something.
In regards to the second, that the crusade was a response to Islamic aggression, this is to be frank an even poorer and more insidious narrative. There was no militarism, aggression, or threat from any Muslims in the area which was conquered by the crusaders, except aggression between competing Islamic polities. This is a fairly straightforward historical truth that was ignored by contemporaries and has become controversial in modern times because of unrelated political and social developments. The origin of the Crusades as an idea developed from military campaigns in Iberia and southern Italy, in which the Papacy officially sanctioned action against Muslim states. It was an established, if nebulous, concept for a couple decades before Alexios Komnenos wrote to Rome asking for military assistance against the Seljuq Turks.
A couple things to make note of in regards to the situation in the Byzantine Empire by the mid 1090s. First, over 20 years had passed since the Battle of Manzikert. Although this is held up as a disastrous moment for the Empire, and indeed was looked upon that way in hindsight by people such as Anna Komnena, the battle itself was less destructive than its aftermath. In fact, it was the political upheaval and internal machinations of the Byzantine elite that led to the collapse of imperial control of Asia Minor. Romanos and the vast majority of his army eventually left the battlefield intact, but civil strife following his usurpation gave the Seljuq’s the opportunity to move into Asia Minor en masse.
By the time of Alexios’s letter, the worst had passed and the situation had been somewhat stabilized. At the very least, it was extremely unlikely that Constantinople would be under direct threat. Furthermore, some of the most desperate fighting in the intervening years had not been against the Seljuqs but instead against invading Normans led by the Guiscard family, which had successful conquered Arab, Lombard, and Greek statelets in Italy. Alexios had fought a fierce war with the Normans throughout the Balkans in order to maintain his European possessions, even as Seljuqs settled comfortably into Anatolia. One of the leaders of the Norman expedition? Bohemond of Taranto.
Second, what Alexios was asking for was not what actually occurred, and the result was certainly not remotely related to Byzantine needs and strategic goals. What Alexios needed and wanted were mercenaries that he could use to begin taking back territory in Asia Minor that had been lost to the Turks. What he emphatically didn’t want or need was the mass of largely unarmed, untrained people who arrived in Constantinople, nor the egos and rivalries of the barons who showed up ostensibly to assist, but with their own agendas both righteous and selfish. There was very little coordination between the crusader armies and the Byzantine army led by Tactikios. Furthermore, as early as the aftermath of the Battle of Doryleum but especially by the time of the Siege of Antioch, it was clear that crusader aims did not align at all with Byzantine. What needed to happen for the security of the Empire to be guaranteed was the seizure and especially the holding of the Anatolian interior so that they could be stabilized and reorganized under imperial rule. However, this was unacceptable to the crusaders for various reasons. The Byzantines did not allow them to plunder the towns they took in Asia Minor, and the Seljuqs did their best to remove and destroy anything of value as they retreated, especially water sources. Most importantly however the crusaders saw their goal as fulfilling a pilgrimage to Jerusalem and so had little interest in staying in what was becoming poor, depopulated land. The severing of Byzantine and crusader goals was completed at Antioch, where both sides became convinced the other was betraying them. In time some crusader states, but especially Antioch, would become an enemy to the empire rather than an ally and asset. In sum, it simply cannot be said that the crusade was a specific, targeted, and effectual response to any Muslim aggression either in intent or in outcome.
Sources for the above include The Alexiad by Anna Komnena, Warren Treadgold’s A History of the Byzantine State and Society, Steven Runciman’s The First Crusade, and Carole Hillenbrand’s The Crusades: Islamic Perspectives
To be honest, neither of them are very appropriate because they completely neglect the complicated context and manifold traditions that the crusading ideology arose from, not least the intense religiosity of the period.
I'm going to do an analysis of the origins of the Crusading ideology - where it came from, how it was expressed etc. I'm going to do this because of how important and varied the context is, which has to be covered before I answer the question. I might come back later and do more, but it's 1am as I start to write this, and I have to drive my a friend to his gig in the morning.
Note: When I say Christian, I will be referring to that of Catholic Europe, any references to Orthodox Christianity and the Byzantine Empire that it primarily existed under will be explicitly labeled.
The Birth of Crusading Tradition
The First Crusade can can be described in various ways – a quest for spiritual redemption, a sanctified outlet for the endemic violence of the European martial classes, and an unprecedented outbreak of religious intensity; what all of these elements have in common is that they exist within the ideological realm. Those who participated in the Crusade were motivated to travel thousands of miles to fulfil the vow that they took voluntarily and as such its hard to overstate the significant of mindset and outlook of the participants - the ideological realm plays a huge part in this.
Christendom on the eve of the Crusades
Evidence for how Muslims were perceived:
Conception of Muslims in literature
Main Sources: Concerning Heresy by John of Damascus and The Apocalypse of Pseudo-Methodius
Muslims were not framed in a complementary manner within the Christian worldview. There were pre-existing religious texts that tackled the issue of apparent Muslim success at Christianity's expense.
Conception of Muslims in vernacular oral poetry
Main Sources: The 'Chanson de Roland'; the ‘Poema de Mio Cid’.
Muslims were already stylised in popular literature as a grand archetypal villain.
The Inception of the Crusade
Main Sources: Western Society and the Church in the Middle Ages by R. W. Southern; The First Crusade: The Call from the East by Peter Frankopan; God's War: A New History of the Crusades by Christopher Tyreman; The Two Cities: Medieval Europe 1050-1320, 2nd Edition; How to Plan a Crusade by Christopher Tyreman; The Crusades: 1095-1198 by Johnathan Riley-Smith in The New Cambridge Medieval History Volume 4 Part 1; The First Crusade and the Idea of Crusading by Johnathan Riley-Smith.
Church Context and Motivation for the Crusading Ideology
Urban II's Specific Theology of War for the First Crusade
Main sources: War, peace and Christian order by Ernst-Dieter Hehl in The New Cambridge Medieval History Volume 4 Part 1; The First Crusade and the Idea of Crusading by Johnathan Riley-Smith;* Western Society and the Church in the Middle Ages by R. W. Southern; God's War: A New History of the Crusad*es by Christopher Tyreman.
The Response
Main Sources: Western Society and the Church in the Middle Ages by R. W. Southern; The First Crusade: The Call from the East by Peter Frankopan; God's War: A New History of the Crusades by Christopher Tyreman; How to Plan a Crusade by Christopher Tyreman; The Crusades: 1095-1198 by Johnathan Riley-Smith in The New Cambridge Medieval History Volume 4 Part 1; The First Crusade and the Idea of Crusading by Johnathan Riley-Smith;* The Social Structure of the First Crusade by Conor Kostick, Holy Warriors: A Modern History of the Crusades by Johnathan Phillips; The First Crusa*de by Thomas Asbridge.
Conclusion
In short, you can see how, in the end, absolutely everything is couched within the religious framework of the day once you dig deep enough. The literature's objection to Muslims was that either that they weren't Christian, or that they were immoral - which was judged by the standards of the Bible; the Crusading ideology itself was born out of movements within the Catholic Church and crystallised by Urban II; and the response was for primarily spiritual reasons.
Proto-colonialist Christendom just doesn't work in this spiritual context. Defensive campaigns against Islam are more tricky, but it doesn't really apply either as:
Anyway, I'm off to bed. I probably won't be able to check this for about half a day, but please to tell me if you find a mistake.
I hope this answer is useful.
Hey! Unfortunately I'm out on the river for the weekend and can't write up a longer response, but you may be interested in the FAQ, in particular this answer I wrote on whether or not the First Crusade was understood as a defensive war.